Glory of the Ny'alotha Raider

Breakdown of each achievement rather than having to go to each of them.

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• Smoke Test - [npc=156818]
  Very simple, just get 3 quick moving dps to stand in the scale drop in Phase 2, then all 3 start hitting Shards at the same time, as long as each of the 3 hit 4 each in 3 seconds you will get this achievement.
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• Mana Sponge - [npc=156523]
  Let the 3rd add that spawns catch a blue orb in Phase 2 (keep it in a void circle until Phase 2 to avoid damaging it), it will transform, pop lust and drag add away for the dark manifestations cast so people can still break stone without taking extra damage, finish Phase 2, kill add then kill boss.
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• Phase 3: Prophet - [npc=161901]
  There is an add, far north on the right side of your map called the Disciple of the Prophet. Kite him into the boss room and damage him down to about 10% (ready to kill). Pull the boss and hero. The add will split into 3. Kill the one add that is really low and start working on the other 2. Once they are dead you can finish the fight as normal.
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• Buzzer Beater - [npc=156575]
  You need to have 2 people bounce the ball close to the portal that you need to get the orb in, the orb needs to go into the portal with less than 3 seconds on your void buff.
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• Total Annihilation - [npc=157354]
  Stack raid and have a monk mass dispel and priest follow up, this will need to happen with 2 annihilation, 1 annihilation is 20 stacks. Big healing CDs, DH Darkness, etc. As long as people get their 30 stacks before they die the achievement will still count. Mark 2 markers, one for raid to stack on and one for purple circles to run to directly behind so that they still get hit with the beam.
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• Realizing Your Potential - [npc=157254]
  You have to find three Promising Specimen in the raid. We found them in entrance corridor to Hivemind on the left hand side, the entrance corridor to Xanesh on the right hand side, and down below near the tentacles on the right hand side as you get to the butt whole. When you click the buff you gain one of three unique Buffs - Carrying a Specimen. When three people have the buff from the three Specimen you pull the boss, although you can just have one person get all 3 and it still counts. The Evolved Specimen spawn from the players with the buff when the first lot of adds spawn. Stack them with the bosses and kill them with the other adds.
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• How? Isn't it Obelisk? - [npc=156866]
  Kill Blue orb first then bounce the soaking circles onto an obelisk to explode it. You will need 5 people to do this as the orb bounces 5 times. You can still soak it when it is under the obelisk. We found keeping the boss in the center of the room made the fight less messy but you can move him to each of the obelisks respectively to make hitting it quicker.
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• You Can Pet the Dog, But... - [npc=157231]
  You can't all /pet at once, start in Phase 2 and go through one by one, 3 seconds in between. The debuff is a ticking dot that will last until he is dead and everyone needs to have this debuff when he dies. Immunities will get rid of it so if you have to bubble, ice block or turtle make sure you /pet him again before the kill. You must be in melee when you /pet him to get the debuff.
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• Temper Tantrum - [npc=157602]
  Kill the first 2 tentacles that are up at the start then mark 2 to kill in the next spawn. Get all others low but do not kill. When 6 are up and low mark 1 tentacle and kill that, wait for Throws of Agony to finish then kill 5 more tentacles, this will make him do Throws of Agony again, then kill boss as per normal.
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• Bloody Mess - [npc=158328]
  Don't interrupt the organs in Phase 2, wait for 12 Bloods to spawn (4 casts going off), group them up and kill them all, remember dispels on fixated targets to reduce damage and use defensives when killing them due to the kill burst. If the 3 people fixated run to center and a druid mass roots them there, it will control them nicely. No damage on bloods before all 12 spawn and you can get one organ low while accumulating Bloods but don't kill it until after you kill the 12 Bloods within 3 seconds, then complete the fight as per normal.
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• Cleansing Treatment - [npc=157439]
  Get all growths low in Phase 2 and then call when to kill them all, one person per growth NO DOTS, NO PETS AND DON’T HIT GROWTHS WHEN SHEILDED. I cannot stress this enough, if one of the growths dies early you have to reset and try again, it may take a few attempts, remember to use your cloak if your sanity is getting low.
  
• It's Not A Cult - N'Zoth the Corruptor
  Do boss as per normal until 20% then don’t stand in the Thought Harvester's circle (a less risky way is to let 2 adds spawn and then let them get the circle cast off with no one standing in them, this will reduce everyone's sanity by 100 at the same time) then pop lust and kill boss. You can get 0 sanity in last phase and then die and it will still count but everyone needs to get to last phase and then 0 sanity before dying or killing the boss.

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• Wrathion: Smoke Test
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• Maut: Mana Sponge
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• The Prophet Skitra: Phase 3: Prophet
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• Dark Inquisitor Xanesh: Buzzer Beater
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• Vexiona: Total Annihilation
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• The Hivemind: Realizing Your Potential
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• Ra-den the Despoiled: How? Isn't it Obelisk?
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• Shad'har the Insatiable: You Can Pet the Dog, But...
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• Drest'agath: Temper Tantrum
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• Il'gynoth, Corruption Reborn: Bloody Mess
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• Carapace of N'Zoth: Cleansing Treatment
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• N'Zoth the Corruptor: It's Not A Cult
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Every achievement is soloable from this meta except probably Cleansing Treatment.

But even that achievement is not necessarily impossible to solo in theory, it's just probably incredibly difficult as you have 10 seconds to kill a bunch of adds that are on the opposite sides of the room and are obstructed by slowing mechanisms.